The Commonwealth Bank (CBA) has given in to Finance Sector Union demands that it change its social media policy, after complaints that the document was too restrictive on employees.

The former policy, provided to ZDNet Australia by the union, had said that employees "must not allow any use of social media channels (such as Facebook or blogs etc) to have an adverse impact on [their] work".

It warned that inappropriate content could adversely affect the group's brand image, and said that employees "must not" use social media channels to "comment on, post or store information about Bank-related matters", speak adversely about the group or post information belonging to the group that was not already publically available.

Breach of the policy was considered to be a "serious disciplinary matter" that could ultimately result in the termination of employment with the bank.

The bank also said that employees should immediately notify their manager and the media and communications team if they became aware of any inappropriate comments made by friends or other people on the social media network.

"You must also provide the Group with all reasonable assistance in relation to any investigation into such material and in relation to the removal of deletion of such material."

The union wrote in a letter in February that it felt that this was too far-reaching, covering any number of innocent posts such as "a conversation about the colour of tea cups in the workplace", and said that it felt that to enforce notification of other people's social media activity went beyond contractual obligations.

Now the union has said that the bank has come up with a new policy, which Finance Sector Union national secretary Leon Carter felt was a significant improvement on the first version.

The wording is softer, he said, talking about common sense in terms of brand reputation. Employees were still told not to post information belonging to the group and speaking disparagingly of the group, but the phrase about commenting on bank matters was qualified to making remarks "in a way that may damage the group".

Although it still requests that employees notify the media team if adverse comments are being made by other people, the requirement has been removed, to be replaced with the phrase "it would assist us if you would".

The policy was also changed so that employees could comment on the terms of their employment.

"CBA's policy now reflects employees' rights to organise and engage with their union colleagues online, and the bank's employees can no longer be held accountable for the actions of others," Carter said in a statement.

"This is a significant shift from the policy that was originally proposed and opposed by union members, and goes to show that even the largest employers can be made to rethink their decisions."

However, Carter cautioned employees that they should still exercise caution with what they posted online, saying that if they wouldn't say something out loud, they shouldn't post it.

The bank acknowledged receiving correspondence from the union about the policy, and said that it had amended the policy two days afterwards. CBA also said that it has altered the policy further since then, with what it considered "minor changes" to "ensure that the intent of the policy is clear".

"Commonwealth Bank will continue to engage with customers through social media channels and listen to customer feedback, provide customer support and assist in finding outcomes for customer circumstances. We hope our team continue to identify and communicate customer issues," the bank said in a statement.

The union said that were no significant changes in the policy it had received on 4 February, and it had continued to press the bank for changes. It said that it had received the current version earlier in the month.